Hidden Markov Models of Strategic Information Control

A stochastic process impinges on an agent and a principal in distinct ways. From the agent's perspective the process is noise that interferes with his perception of productivity states, leading him to sometimes take actions that are in retrospect mistaken. From the principal's perspective the noise is in fact the productivity of the agent's action, and he would like to coordinate the agent's actions with the process. The principal is not able to provide direct material payoffs to the agent in order to induce this coordination. He is however allowed to communicate with the agent. If he fully communicates the state of the noise process, the agent will eliminate all response to it, thus vitiating the principal's interests. If he communicates nothing, the agent's reactions to the noise are random, and will be in synchrony with the principal's interests only by accident. The principal can send a Pareto-improving signal however. Such a signal requires that the agent from his perspective make mistakes, and fails to fully coordinate actions with states from the principal's perspective. The strategic use of information is modeled using a hidden Markov model framework. In this framework, the state of a Markov process is unobservable, but it drives a signal that is correlated with it. This framework allows the agent's optimization problem to be simplified using a measure change (which may be familiar to some readers as a Girsanov transformation). The simplified representation of the agent's problem then becomes a set of constraints for the principal. The key methodological innovation here is that the informativeness of the signal is directly controllable by the principal. The informativeness is represented by elements of a matrix, reducing the information strategy to choosing elements of the matrix